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Preprint Sep 2026

Determinantal Kernel Schemes of Matrix Nets and Applications to Positive Maps

For a linear map on a matrix space, we study the projective schemes obtained by intersecting its projectivized kernel with determinantal rank loci. For matrix nets, that is, three dimensional matrix spaces, we classify every positive dimensional intersection with the rank one Segre variety in arbitrary rectangular size...

T. Dinh, Minh Toan Ho, Cong Trinh Le et al. · 0 citations
Preprint Sep 2026

Frobenius dilation of Hilbert function, Demailly's conjecture, and varieties of powers

We prove a Frobenius-dilation inequality for Hilbert functions of ideals generated by powers of fixed homogeneous forms in characteristic zero. Via Emsalem--Iarrobino inverse system duality, it yields quantitative fat-point postulation estimates and a new proof of the recent theorem of Ha--Sivakumar resolving Demailly'...

T. Dinh, Tài Huy Hà · 2 citations
Preprint Sep 2026

Demailly's Conjecture in Quantum Language and Its Solution

We give an exact translation between fat-point interpolation in complex projective space and a dark-state problem for fixed-particle-number bosons. Under the unitary Fischer--Bargmann realization, homogeneous degree becomes particle number, the Veronese lift becomes a bosonic symmetric product state, and order-$m$ vani...

T. Dinh · 0 citations

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